Question

11-8. Equation (11.4) is an expression for the energy levels of the delocalized MOs for a conjugated chain of N carbon atoms. In the limit of a very long chain of length L, with a LIN the distance between neighboring carbon atoms, this equation becomes E = α + 2β cos(ka), with k = π/L, 2π/L, 3 π/L, . NTIL Tla). (Yes, k is the wave number of the "waves" represented by equation (11.5)-see discussion at the end of Section 11.3.) (a) Assuming that N is so large that the energy levels can be considered to form a con- tinuous energy band, and that k is a continuous rather than a discrete vari- able, derive an expression for the group velocity of electrons in this band. (b) Sketch the variation of energy and group velocity with k from the bottom (k 0) to the top (k la) of this band. Jm 12. 3....NMy

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